Phi or the golden ratio

For, about 2400 years, humans are fascinated with the number Phi which is calculated as (1+ square root of 5) divided by 2 giving us the result of 1.61803...
Not only is this ratio often used in art, architecture and design, but is also seems to be a common ratio in nature.
What do you think, is the occurrence of the golden ratio in nature just a coincidence or is there more to it ?
If so, what could explain that that this ratio is so common in nature ?

Nov 7 2013:
Two things can explain why phi is so common in nature.
1. Ask why mountains are mostly cone shaped. 'Phi' may be common in nature as the spatial growth of complex biological systems finds this ratio as the simplest expansion route. It may be argued that other different proportions were blindly tried by nature and they just lost out in the evolutionary trial and error.
2. Another somewhat different but equally plausible cause is related to the fact that most often the claims of accuracy of the proportions in natural bodies to be exactly phi is inaccurate. Arts and architecture are different, they are intentionally created to match this ratio. But on account of a phenomenon called pareidolia our pattern seeking brains conjure up this ratio in nature.
Fritzie's comment is interesting, thanks to her.

Nov 7 2013:
There's nothing more satisfying than conceptually describing nature through symmetries, unifying measures and amounts in relation. It gives a sense of control and provides a tolerable paradigm through which we create and interact with the natural world.

The following is a poem I wrote a while back that further illustrates my point:

Groups that Lie, Root their Systems in Vectors gone awry
Conflicts arise, as manifest patterns become the linear structures for life to survive.
Of salient transcription, notational in and of the principally framed
We seek to maintain grandiose, semiotic paradigm's begetting invariant claims
Dimensionally unified, the intangible are expressed by the formulations of mind
Fighting for stasis, a basis for attaining solidification of place in time.

The following video will most likely answer most Harald Jezek's questions:

Nov 7 2013:
Pabitra, as to point 1: yes this might be a possibility. Are you aware of any studies on this topic ?
As to point 2: This is certainly true. Even in the case of the Fibonacci numbers the ratio between one and another one is not exactly Phi.

The golden ratio is simply the ratio of the long side to the short side of the "brick." Many people believe these proportions are more visually appealing than longer skinnier rectangles or more square ones.

Another entry point in thinking about phi starts with the Fibonacci numbers, which many of the younger people here have probably seen. The sequence goes 1 1 2 3 5 8 13 21 34 and so forth. The rule for making this sequence is easy to see if you look at any three consecutive numbers in the series. Add the first two and you get the third. If you count the number of little sections in the rows of pineapples and pine cones, they pretty much follow a fibonnacci sequence. And as you keep generating more numbers in that sequence, you find that the ratio of a fibonacci number to the one before it gets closer and closer to phi as the numbers get larger.

Nov 7 2013:
Absolutely correct Fritzie. So why is this number so prevalent in mathematics and nature ? Or is it just that humans always look for patterns and phi is just one that simply pops up because people for some reason focused on it ?

Nov 7 2013:
I have a feeling there is some sort of evolutionary explanation for why the particular symmetry of the golden rectangle would have peculiar aesthetic appeal. It is probably something like that this rectangle approximates the aspect ratio of a newborn baby in its natural position with little knees pulled up. I just measured the dog, and she has pretty much this aspect ratio as well when standing.

The reason I mentioned the Fibonacci sequence is that seeing that the rule for generating the next number on the list has such a simple sort of form makes it easier to believe such a pattern might be common in nature. Similarly, seeing a visual representation of the square, the triangular, and the hexagonal numbers makes it easier to see why those also might appear commonly in nature.

It only seems bizarre when you look at the numbers without the simple generating algorithm.

Nov 7 2013:
I don't remember Phi from Dan Brown's novels but only the Fibonacci numbers. Btw, I'm just watching the video for which John provided the youtube link. I'm only half way through but it seems interesting and worth watching.

Nov 7 2013:
Keith Devlin does wonderful, well-written work aimed at the math enthusiast (who is not required to be thoroughly versed in mathematics).

I would not remember either from Angels and Demons except that, as a former math teacher, I knew whenever I assigned students to write a short article on an interesting idea in mathematics (which I needed to approve to avoid redundancy), the first topic any student put forward was always phi, because they had all read much about it in Dan Brown.

Nov 20 2013:
On YouTube I saw a video posted by a girl called 'VI Hart' and in her videos (three in total) she explains the occurrence of these phenomenon in nature. Basically it comes down to this: a plant wants to get the most possible out of it leaves, meaning it wants to obtain the most sunshine for photosynthesis that it can on each leaf (well some plants but not all). So what the plant does is it distributes it's leaves as far away from each other as possible without it going closer to another leaf. Now in the video it is explained completely but it ends up that the degree between each leaf will distribute certain patterns in rows and diagonals which can be related with the Fibonacci sequence or with Phi .

Nov 18 2013:
"Why" indeed! Thanks for asking that. I truly wish I could be of help here.
Perhaps it's just the sub-atoms making use of the various sub-atomic forces efficiently - you know - those crazy lines that come out of atom-smashers.
My only other guess is that is how we want to see the measurements come-out; as even measurements are guesses, (biased guesses in the end), if you look close-enough.
BTW, the best "Why" I've found so-far, by-far, is Stan Tenen's Meru Foundation work. (That is, "if you're tired of the rusty-old gold or platinum explanations.")

Nov 15 2013:
The way I like to make sense of it in my own thought process is this; every task we perform we try to find the most efficient way to do it. If you were tasked with moving a mound of dirt from point A to B you probably wouldn't do it by the handful or bucketful. You would find a suitable container to load it into that would move that dirt with the least amount of effort. Work smart so you're not working too hard.

Nature has figured out the most effective way to grow things. There is some efficiency connected to this particular calculation that provides nature with the most efficient way to produce and grow.

Nov 13 2013:
It seems Nature reuses all her mathematical tricks. The equations that describe the ripples in the sand at low tide also describe the pattern of stripes on a zebra, (or a tiger, I forget). The equations that describe the position of prime numbers on the number line also precisely describe the sub atomic behaviour of certain heavy elements.

Makes sense if the universe is computing reality as it goes along.
Information using energy to produce complexity.

Nov 14 2013:
Agreed, and perhaps the deeper we dig into mathematics the more we need to see "number" as a driver in itself. Not a force or an energy as such, not a dumb tool; but as something deep in the fabric of things.

A crude analogy with a computer maybe, the energy is electrical, the "force" is human, the tools are logical programs and the output is to all intents and purposes magical, but the engine is pure number in ordered motion.